MHB How to Expand Algebraic Identities

[NotaMathPerson]

Hello! Please help me start solving this.

View attachment 5567

I did expand the lhs but I still can't make it to be like the rhs. Any help would be appreciated!

 

[Opalg]

There may be neater ways to do this, but you can't go wrong if you simply multiply out the brackets on both sides and see whether they give the same answer.

 

[Deveno]

Hint: expand the right-hand side, first. You'll find some stuff "cancels".

 

[suluclac]

According to Opalg, you probably know (m + n)² = m² + 2mn + n².
Also, $$(w+x)(y+z)=wy+xy+wz+xz$$.
Therefore, $$(wy+xy+wz+xz)(\alpha+\beta)=\alpha wy+\alpha xy+\alpha wz+\alpha xz+\beta wy+\beta xy+\beta wz+\beta xz$$.